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Gregor Mendel's Genetic Experiments A Statistical Analysis after 150 Years

Author(s): Jan Kalina

Gregor Mendel is generally acknowledged not only as the founder of genetics but also as the author of the rst mathematical result in biology. Although his education had been questioned for a long time, he was profoundly educated in botany as well as physics and in those parts of mathematics (combinatorics, probability theory) applied in his later pea plants experiments. Nevertheless, there remain debates in statistical literature about the reasons why are Mendel's results in such a too good accordance with expected values [22, 28]. The main aim of this paper is to propose new two-stage statistical models, which are in a better accordance with Mendel's data than a classical model, where the latter considers a xed sample size. If Mendel realized his experiments following such two-stage algorithm, which cannot be however proven, the results would purify Mendel's legacy and remove the suspicions that he modi ed the results. Mendel's experiments are described from a statistical point of view and his data are shown to be close to randomly generated data from the novel models. Such model is found as the most suitable, which is remarkably simpler according to the model of [28], while the new model yields only slightly weaker results. The paper also discusses Mendel's legacy from the point of view of biostatistics.


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